\(\left\{{}\begin{matrix}x+my=2\\mx-2y=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}mx+m^2y=2m\\mx-2y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2-my\\\left(m^2+2\right)y=2m-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2-my=\frac{m+4}{m^2+2}\\y=\frac{2m-1}{m^2+2}\end{matrix}\right.\)
Để \(\left\{{}\begin{matrix}x>0\\y< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\frac{m+4}{m^2+2}>0\\\frac{2m-1}{m^2+2}< 0\end{matrix}\right.\) \(\Rightarrow-4< m< \frac{1}{2}\)
